This study presents the initial results of developing a technology for synthesizing a flexible superconducting magnesium diboride composite on a Hastelloy®-C276TM substrate coated with Al2O3/Y2O3/MgO/LaMnO3 buffer layers. The superconducting composite was deposited by magnetron sputtering from two Mg and B targets, followed by vacuum annealing at various substrate temperatures ranging from 400 °C to 700 °C. The superconducting transition temperature T
c ≈ 22 K, with a transition width ΔT ≈ 1 K, and critical current J
c ≈ 500 kA cm−2 (T= 5 K, H = 2 T) and J
c ≈ 11 kA cm−2 (T = 15 K, H = 2 T) at the optimal annealing temperature of 400 °C.